Browsing by Author "Hwang, CW"

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A method for computing the coefficients in the product-sum formula of associated Legendre functions
(1995-11-01)
Hwang, CW
;
交大名義發表
;
土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
The product of two associated Legendre functions can be represented by a finite series in associated Legendre functions with unique coefficients. In this study a method is proposed to compute the coefficients in this product-sum formula. The method is of recursive nature and is based on the straightforward polynomial form of the associated Legendre function's factor. The method is verified through the computation of integrals of products of two associated Legendre functions over a given interval and the computation of integrals of products of two Legendre polynomials over [0,1]. These coefficients are basically constant and can be used in any future related applications. A table containing the coefficients up to degree 5 is given for ready reference.
A study of the Kuroshio's seasonal variabilities using an altimetric gravimetric geoid and TOPEX/POSEIDON altimeter data
(1996-03-15)
Hwang, CW
;
交大名義發表
;
土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
The first year of TOPEX/POSEIDON (T/P) altimeter data were used to study the seasonal variabilities of the Kuroshio Current. The intercomparison between the T/P and gauge sea levels at selected tide gauge stations around Taiwan shows that the two have a correlation of about 0.9 at the immediate vicinity of the deep ocean and both show an annual cycle with an amplitude of 15 cm. A 3' x 3' geoid for the Western Pacific was constructed by least squares collocation using gravity anomalies and sea surface gradients derived from Seasat, Geosat, ERS 1, and T/P altimetry. To account for the oceanographic signal in the altimeter data, we derived a covariance function for the gradients of the sea surface topography (SST) based on a global averaging concept and a spherical harmonic expansion of the Levitus SST to degree 50. The accuracy of the geoid ranges from 5 to 40 cm. The SST values derived from the geoid and the data along T/P's descending tracks were fitted to the hyperbolic functions in a two-step procedure to find the Kuroshio's seasonal axes and the parameters that describe its characteristics. The mean variabilities in the Kuroshio's path, maximum velocity, baroclinic transport, and width are 22 km, 19 cm, 8 Sv, and 27 km, respectively. The averaged percentage variability of all quantities is 25%. All the variabilities are relatively large near the northeast coast of Taiwan and the starting point of the Kuroshio Extension. The large-scale circulations over the Western Pacific were obtained by median filtering the SST. At the 1334-km spatial scale, the Pacific's subtropical gyre is clearly visible, and it shows different features over the four seasons and its kinetic energy shows possible correlations with the determined parameters. Over the South China Sea a warm ring with a radius of 300-400 km and a center at 15 degrees N, 113 degrees E was detected in the spring and summer.
Adjustment of relative gravity measurements using weighted and datum-free constraints
(2002-11-01)
Hwang, CW
;
Wang, CG
;
Lee, LH
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土木工程學系
;
Department of Civil Engineering
A program in FORTRAN 90 is developed which can adjust relative gravity measurements and solve for gravimeter parameters using the weighted constraint and datum-free constraint models. The weighted constraint model is chosen when there exist reliable a priori gravity values for use as supplementary data, or when it is required that a gravity network be attached to an existing gravity network of a higher order. The datum-free model uniquely determines relative gravity values among all stations without the need of a fixed gravity value, thus it is suitable for detecting relative gravity change. The optional solve-for gravimeter parameters include drift coefficients, and coefficients of the long wavelength and periodic components of calibration function. The program can also detect outliers in observations using the T-test method. A set of relative gravity data in Taiwan was used to test this program using five different choices of command-line arguments. The results show that there are no outliers in these data and that the estimated reading accuracy of the LaCoste and Romberg G meter (serial number 838) is about 0.02 mgal and the gravimeter drift rate is 0.9 mgal/month. The coefficients of the long wavelength and periodic components of calibration function are statistically equal to zero. The result from the datum-free solution is used to detect gravity variation due to the 1999 Chi-Chi earthquake, concluding that only one station experiences a significant change. (C) 2002 Elsevier Science Ltd. All rights reserved.
An optimal procedure for deriving marine gravity from multi-satellite altimetry
(1996-06-01)
Hwang, CW
;
Parsons, B
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土木工程學系
;
Department of Civil Engineering
An optimal procedure is developed for deriving gravity anomalies from sea-surface height measurements obtained by a number of different satellites, the inclinations of which may vary. We begin by recasting the problem of the conversion of the deflection of the vertical to gravity in the frequency domain. We show that a deterministic approach based on the Vening-Meinesz integral is equivalent in the frequency domain to the stochastically based method of least-squares collocation. A new method for gridding the deflection of the vertical is developed that uses the fact that satellite tracks of the same type (ascending or descending) are nearly parallel, so that values at grid points can be estimated by first performing along-track interpolations, followed by one cross-track interpolation, both using Akima's spline. This gridding method is very efficient compared with methods such as that of fitting minimum curvature surfaces, especially for dense data such as for the 168 day cycles of ERS-1. A weighted least-squares method is then employed to obtain the north and east components of deflection-of-the-vertical components using the gridded along-track components from all of the individual satellite missions. Finally, gravity anomalies are computed from the two deflection-of-the-vertical components in the frequency domain with truncated kernel functions, the use of which is related to the prior removal of a high-degree reference gravity field. This new procedure is more than 100 times faster than least-squares collocation, and yields gravity anomalies with errors that are comparable to those derived by least-squares collocation and smaller than those derived by other recent applications of spectral techniques, as judged by comparisons with ship-gravity measurements. The case of gravity computation for a single altimetric satellite is handled separately, and a method is given to estimate the noise spectra of deflection of the vertical and reduce the numerical problems caused by satellites with high inclination angles. The new procedures make possible quick, yet accurate, global updates of the marine gravity field.
An optimal procedure for deriving marine gravity from multi-satellite altimetry
(1996-06-01)
Hwang, CW
;
Parsons, B
;
土木工程學系
;
Department of Civil Engineering
An optimal procedure is developed for deriving gravity anomalies from sea-surface height measurements obtained by a number of different satellites, the inclinations of which may vary. We begin by recasting the problem of the conversion of the deflection of the vertical to gravity in the frequency domain. We show that a deterministic approach based on the Vening-Meinesz integral is equivalent in the frequency domain to the stochastically based method of least-squares collocation. A new method for gridding the deflection of the vertical is developed that uses the fact that satellite tracks of the same type (ascending or descending) are nearly parallel, so that values at grid points can be estimated by first performing along-track interpolations, followed by one cross-track interpolation, both using Akima's spline. This gridding method is very efficient compared with methods such as that of fitting minimum curvature surfaces, especially for dense data such as for the 168 day cycles of ERS-1. A weighted least-squares method is then employed to obtain the north and east components of deflection-of-the-vertical components using the gridded along-track components from all of the individual satellite missions. Finally, gravity anomalies are computed from the two deflection-of-the-vertical components in the frequency domain with truncated kernel functions, the use of which is related to the prior removal of a high-degree reference gravity field. This new procedure is more than 100 times faster than least-squares collocation, and yields gravity anomalies with errors that are comparable to those derived by least-squares collocation and smaller than those derived by other recent applications of spectral techniques, as judged by comparisons with ship-gravity measurements. The case of gravity computation for a single altimetric satellite is handled separately, and a method is given to estimate the noise spectra of deflection of the vertical and reduce the numerical problems caused by satellites with high inclination angles. The new procedures make possible quick, yet accurate, global updates of the marine gravity field.
COSMIC: Geodetic applications in improving earth's gravity model
(2000-03-01)
Chao, BF
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Pavlis, EC
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Hwang, CW
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Liu, CC
;
Shum, CK
The routine GPS tracking data that will be collected for the precise orbit determination of the eight COSMIC spacecraft will contain valuable information about the terrestrial gravity field. Numerical simulations based on current straw-man mission scenarios have shown: (1) For the static model of the gravity field, significant improvement is possible over our present knowledge embodied in the EGM96 model, out to harmonic degree as high as 40. (2) With respect to time-varying gravitational signals, large-scale mass transport processes in the geophysical fluids (e.g., atmosphere and oceans) can be detected or monitored during the mission, providing important global change information. Further sophisticated simulations incorporating more realistic force models will be needed once COSMIC mission scenario and spacecraft design are completely defined.
Fully normalized spherical cap harmonics: Application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1
(1997-05-01)
Hwang, CW
;
Chen, SK
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交大名義發表
;
土木工程學系
;
National Chiao Tung University
We introduce two sets of fully normalized harmonics for the spectral analysis of functions defined on a spherical cap. The harmonics are the products of Fourier functions and the fully normalized associated Legendre functions of non-integer degree. Using Sturm-Liouville theory for boundary-value problems, we present two convenient and stable formulae for computing the zeros of the associated Legendre functions that form two sets of orthogonal functions. Formulae for the stable numerical evaluation of the fully normalized associated Legendre functions of non-integer degree that avoid the gamma function are also derived. The result from the expansions of sealevel anomaly from altimetry into Set 2 fully normalized cap harmonics shows fast convergence of the series, and the degree variances decay rapidly without aliasing effects. The zero-degree coefficients (Set 2) of sea-level anomaly from TOPEX/POSEIDON (T/P) and ERS-1 indicate an El Nino event during 1993 January-1993 July, and a La Nina event during 1993 November-1994 July, although the ERS-1 result is less obvious. Ocean circulations over the South China Sea and the Kuroshio area are clearly identified with the low-degree expansions of sea-surface topography (SST) from T/P and ERS-1. A cold-core eddy of 4 degrees in diameter centred at 17.5 degrees N, 118 degrees E was detected with the expansion of SST from T/P cycle 47, and a property of the cap harmonics is used to compute this eddy's kinetic energy. The kinetic energy is at a low in winter and high in summer, and its variation seems to be periodic with an amplitude of 0.4 m(2) s(-2).
Height system of Taiwan from satellite and terrestrial data
(1997-11-01)
Hwang, CW
;
交大名義發表
;
土木工程學系
;
National Chiao Tung University
;
Department of Civil Engineering
The global positioning system(GPS), satellite altimetry, tide records, differential leveling, and a geoid model have been used to study the height system of Taiwan, Republic of China. Using the International GPS Service (IGS) orbit, the geocentric coordinates in International Terrestrial Reference Frame (ITRF) and the mean sea levels at six key tide stations around Taiwan were determined by GPS, and this result will contribute data to the permanent service of mean sea level. It is found by detailed field work and calibration that the vertical datum of Taiwan is defined to be the mean sea level of Keelung located at northern Taiwan. The vertical datum undergoes a secular rise at 1.28 mm/year which must be considered in de fining future benchmark heights. It is shown that a good geoid model can be of many uses such as GPS leveling, detecting systematic errors in a leveling net and changes of benchmark heights. The relative sea surface topography (SST) values at tide stations were determined from satellite altimetry and GPS data, and their standard errors are mostly below 10 cm. The SST values are recommended to be used as weighted constraints in the adjustment of a leveling net. A preliminary connection of Taiwan's vertical datum to other regional datums has been examined by computing a global SST at a 600-km wavelength using the EGM96 geopotential model and TOPEX/POSEIDON altimetry.
Lake level variations in China from TOPEX/Poseidon altimetry: data quality assessment and links to precipitation and ENSO
(2005-04-01)
Hwang, CW
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Peng, MF
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Ning, JS
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Luo, J
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Sui, CH
About 10 yr of TOPEX/Poseidon (T/P) altimetry data have been used to compute time series of lake levels at six inland lakes in China. To verify our T/P data processing strategy, the T/P-derived lake levels at Bosten Lake (west China) and Lake Huron (north America) were compared with lake gauge records: good agreement is found between the T/P and the gauge results. Wavelet spectra indicate annual and interannual variations of these lake levels, which are also sensitive to climate variability. At the interannual timescale, the lake levels of Hulun (north China), Bosten (west China) and Ngangzi (east Tibet) are correlated with precipitation and El Nino Southern Oscillation (ENSO); in particular, they all respond to the 1997-1998 El Nino. The Bosten lake level has increased monotonically since 1993 due to the increased temperature on Tianshan Mountain, which feeds water into this lake. The lake levels of Hongze and Gaoyou (east China) show minor decreasing trends. The lake level of La'nga (west Tibet) decreased steadily from 1993 to 2001, with a total drop of 4 m. The Ngangzi lake level decreased from 1993 January to 1997 December, but after the peak of the 1997-1998 El Nino the slope was reversed and the lake level has increased monotonically since then. An example given at Bosten Lake shows that waveform contamination over Chinese lakes affects the quality of T/P-derived lake levels and retracking is necessary to mitigate the problem.
Marine gravity anomaly from satellite altimetry: a comparison of methods over shallow waters
(2004)
Hwang, CW
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Hsu, HY
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Deng, XL
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土木工程學系
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Department of Civil Engineering
Gravity anomalies over shallow waters are useful in many geodetic and geophysical applications. This work compares three methods of gravity anomaly derivation from altimetry over shallow waters near Taiwan: (1) compute gravity anomalies by LSC using along-track, differenced geoidal heights and height slopes, (2) compute gravity anomalies by least-squares collocation (LSC) using altimeter-derived along-track deflections of vertical (DOV), and (3) grid along-track deflections of vertical by LSC and then compute gravity anomalies by the inverse Vening Meinesz formula. A nonlinear filter with outlier rejection is applied to along-track data. We used altimeter data from Seasat, Geosat, ERS-1, ERS-2 and TOPEX/POSEDION missions. Retracked ERS-1 waveforms are shown to improve the accuracy of estimated gravity anomalies. For the three methods, the RMS differences between altimetry-derived gravity anomalies and shipborne gravity anomalies are 9.96 (differenced height) and 10.26 (height slope), 10.44 and 10.73 mgals, respectively. The RMS differences between shipborne gravity anomalies with gravity anomalies from retracked and non-retracked ERS-1 waveforms are 11.63 and 14.74 mgals, indicating retracking can improve the accuracy.
Neutrino-photon scattering and its crossed processes in a background magnetic field
(1999-11-04)
Chyi, TK
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Hwang, CW
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Kao, WF
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Lin, GL
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Ng, KW
We study the neutrino-photon processes such as gamma gamma --> , v gamma --> v gamma, and --> gamma gamma in a background magnetic field smaller than the critical magnetic field Bc + m(e)(2)/e. Using Schwinger's formalism, we extract leading magnetic-field contributions to the above processes. Our result is valid throughout the kinematic regime where both neutrino and photon energies are significantly smaller than m(w). We briefly discuss the astrophysical implications of our result. (C) 1999 Published by Elsevier Science B.V. All rights reserved.
Single- and multiepoch analyses of global positioning system baseline network: Application to coordinate and velocity determinations in Central Taiwan
(2004-05-01)
Hwang, CW
;
Lee, LH
;
Yu, SB
;
Chen, HY
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土木工程學系
Theories and computer programs are developed for single- and multiepoch analyses of a global positioning system (GPS) baseline network using the datum-free and weighted constraint solutions. Single-epoch analysis is for evaluating data quality, removing outliers, examining network precision, and estimating coordinates. Multiepoch analysis is for simultaneously determining epoch coordinates and station velocities. The datum-free solution yields estimable data residuals and relative coordinates and is suitable for adjusting data only and for detecting changes of relative coordinates. The weighted constraint solution allows a lower-order network to be attached to an existing, higher-order network. The analysis methods are applied to a multiepoch GPS baseline network in central Taiwan, which was hit by the 1999 Chi-Chi earthquake measuring 7.3 on the Richter scale. The velocities computed by the methods developed in this study are consistent with those from the Bernese GPS software. The result of the multiepoch analysis indicates that, in the first year after the Chi-Chi earthquake, the crust east of the Chelungpu Fault moved northwestwards at a mean rate of about 10 cm/year, while the crust west of the Chelungpu Fault moved in the opposite direction at a much lower speed.
Terrain correction computation using Gaussian quadrature
(2003-12-01)
Hwang, CW
;
Wang, CG
;
Hsiao, YS
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土木工程學系
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Department of Civil Engineering
A method and a program (tcq) in FORTRAN 90 based on Gaussian quadrature are developed to compute the terrain correction (TC). TCs were determined on 1010 benchmarks using the Gaussian quadrature, prism and FFT methods using a 3" x 3" elevation grid for the inner zone and a 30" x 30" elevation grid for the outer zone. In order to achieve a 0.1 mgal accuracy in TC while reducing the computing time, the best inner and outer radii for TC computation are 20 and 200 km, respectively. The Gaussian quadrature is a highly accurate numerical integrator and yields results that outperform those from the prism method and the FFT method. The singular problem of the kernel function in TC is treated by considering the innermost zone effect, which can be expressed as a complete elliptic integral of the first kind. The innermost zone effect must be taken into account if the required accuracy of TC is at a 1-mgal level. (C) 2003 Elsevier Ltd. All rights reserved.
Use of geoid for assessing trigonometric height accuracy and detecting vertical land motion
(2002-02-01)
Hwang, CW
;
Hwang, LS
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土木工程學系
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Department of Civil Engineering
An improved geoid model for Taiwan was developed using land and sea gravity anomalies and altimeter-derived geoid gradients by least-squares collocation. The estimated model accuracy ranges from 2 cm in the flat area to 10 cm in the mountainous area. This geoid model, along with GPS ellipsoidal heights, is used to determine the errors of the "orthometric heights" at Taiwan's first-order triangulation stations, yielding an RMS error of 0.97 m. Yushan, east Asia's highest peak, is now estimated to be 3,950.50 m above the mean level at Keelung from this geoid model and GPS measurements. With recent measured ellipsoidal heights at 33 benchmarks in eastern Taiwan, an average uplift rate of 4.46 cm/year is found along the Longitudinal Valley, and 3.02 cm/year along the coastal highway. This uplift is the result of the collision between the Philippine Sea plate and the Eurasian plate, and the rates are consistent with those derived from terrestrial measurements and tide gauge records.
Weak-field expansion for processes in a homogeneous background magnetic field
(2000-11-15)
Chyi, TK
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Hwang, CW
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Kao, WF
;
Lin, GL
;
Ng, KW
The weak-field expansion of the charged fermion propagator under a uniform magnetic field is studied. Starting from Schwinger's proper-time representation, we express the charged fermion propagator as an infinite series corresponding to different Landau levels. This infinite series is then reorganized according to the powers of the external field strength B. For illustration, we apply this expansion to gamma --> nu<()over bar> and nu --> nu gamma decays, which involve charged fermions in the internal loop. The leading and subleading magnetic-field effects to the above processes are computed.